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McGraw Hill Glencoe Algebra 1, 2012 View details

3. Solving Multi-Step Inequalities

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Exercise 65 Page 303

What can you do to isolate a variable in an inequality?

{b|b>-4}

Practice makes perfect

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.

12b>-48

DivIneq

.LHS /12.>.RHS /12.

b>-4

This tells us that all values greater than -4 satisfy the inequality. Knowing this, we can write the solution set. {b|b>-4}

Checking Our Solution

We can check our solution by substituting a few arbitrary values into the original inequality. The value satisfies the inequality if the inequality remains true after substituting and simplifying.

b	12b>-48	Evaluate
-5	12( -5)>-48	-60≯-48
-4	12( -4)>-48	-48≯-48
-3	12( -3)>-48	-36>-48

We can conclude that, as long as y is greater than -4, the inequality is satisfied. This means our solution is correct.

Subchapter links

Check Your Understanding p.300

Practice and Problem Solving p.301-302

H.O.T. Problems p.302

Standardized Test Practice p.303

Spiral Review p.303

Skills Review p.303

Exercise 65 Page 303

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Checking Our Solution